# Absence of localization in a disordered one-dimensional ring threaded by an Aharonov–Bohm flux

@article{Heinrichs2009AbsenceOL, title={Absence of localization in a disordered one-dimensional ring threaded by an Aharonov–Bohm flux}, author={Jean Heinrichs}, journal={Journal of Physics: Condensed Matter}, year={2009}, volume={21}, pages={295701} }

Absence of localization is demonstrated analytically to leading order in weak disorder in a one-dimensional Anderson model of a ring threaded by an Aharonov–Bohm (AB) flux. The result follows from adapting an earlier perturbation treatment of disorder in a superconducting ring subjected to an imaginary vector potential proportional to a depinning field for flux lines bound to random columnar defects parallel to the axis of the ring. The absence of localization in the ring threaded by an AB flux…

## 4 Citations

### Flux-free conductance modulation in a helical Aharonov–Bohm interferometer

- PhysicsJournal of physics. Condensed matter : an Institute of Physics journal
- 2010

A novel conductance oscillation in a twisted quantum ring composed of a helical atomic configuration is theoretically predicted. The internal torsion of the ring is found to cause a quantum phase…

### Investigation of Brewster anomalies in one-dimensional disordered media having Lévy-type distribution

- Physics
- 2016

Abstract
In this paper, we calculate the localization length of a TM electromagnetic wave in unit
of system length versus incident angle in a disordered layered structure where the
refractive index…

### Universal shift of the Brewster angle and disorder-enhanced delocalization of p waves in stratified random media.

- PhysicsOptics express
- 2011

It is found that when the average relative dielectric permittivity is less than one and the incident angle is larger than the generalized Brewster angle, both the localization length and the disorder-averaged transmittance increase substantially as the strength of disorder increases in a wide range of the disorder parameter.

### An exactly solvable model for the integrability-chaos transition in rough quantum billiards.

- PhysicsNature communications
- 2012

A simple statistically solvable quantum model describing this memory loss across an integrability-chaos transition under a perturbation obeying no selection rules is presented.

## References

SHOWING 1-10 OF 52 REFERENCES

### FLUX DEPENDENCE OF PERSISTENT CURRENT IN A MESOSCOPIC DISORDERED TIGHT BINDING RING

- Physics
- 2002

We reconsider the study of persistent currents in a disordered one-dimensional ring threaded by a magnetic flux ϕ, using he one-band tight-binding model for a ring of N-sites with random site…

### Theory of Localization in a Disordered Ring in a Non-Hermitian Field

- Physics
- 2002

We present an analytical study of the Lyapunov exponent λ for electronic states in a disordered tight-binding ring, with N sites of spacing c, in the presence of a non-hermitian field component h,…

### Theory of non-hermitian localization in one dimension: Localization length and eigenergies

- Physics
- 2002

We recall some basic aspects of the pinning of flux lines in a superconducting cylindrical shell subjected to a depinning magnetic field, as well as its description by the quantum mechanics of a…

### Theory of directed localization in one dimension.

- Physics
- 1997

We present an analytical solution of the delocalization transition that is induced by an imaginary vector potential in a disordered chain [N. Hatano and D. R. Nelson, Phys. Rev. Lett. 77, 570…

### Diamagnetic persistent current in diffusive normal-metal rings.

- PhysicsPhysical review letters
- 2001

This work has measured a diamagnetic persistent current with flux periodicities of both h/e and h/2e in an array of thirty diffusive mesoscopic gold rings and considers a new approach associated with the saturation of the phase coherence time tau(phi).

### Symmetry and transport of waves in one-dimensional disordered systems

- Computer Science
- 1994

The transfer matrix approach to transport in one-dimensional systems is reviewed in detail with emphasis on the role of symmetrized products, and the problem of 1/f noise in disordered systems is addressed in the language of symmETrized transfer matrices.

### Diamagnetic orbital response of mesoscopic silver rings.

- PhysicsPhysical review letters
- 2002

Measurements of the flux-dependent orbital magnetic susceptibility of an ensemble of 10(5) disconnected silver rings indicate unambiguously diamagnetism in the vicinity of zero magnetic field, a priori not consistent with theoretical predictions for average persistent currents.

### Localization Transitions in Non-Hermitian Quantum Mechanics.

- PhysicsPhysical review letters
- 1996

The theory predicts that, close to the depinning transition, the transverse Meissner effect is accompanied by stretched exponential relaxation of the field into the bulk and a diverging penetration depth.

### Introduction to mesoscopic physics

- Physics
- 1997

Preface Preface to the second edition List of symbols 1. Introduction and a brief review of experimental systems 2. Quantum transport, Anderson Localization 3. Dephasing by coupling with the…

### Localization: theory and experiment

- Physics
- 1993

The transport properties of disordered solids have been the subject of much work since at least the 1950s, but with a new burst of activity during the 1980s which has survived up to the present day.…